New data on trace element partitioning in the Fe-Ni-S-P system suggest that iron meteorites of groups IAB and IIICD come from one or more S-rich parent bodies. Heating of the IAB parent body melted all troilite, but caused only very minor partial melting of silicates. Cocrystallization of metal and troilite produced the high-Ni ''tail'' of group IAB. The trace element patterns are consistent with a parent body with CI sulfur and siderophile abundances. Compositionally the parent body was intermediate between ordinary and E4 chondrites, its thermal history was in between ordinary chondrite and fully differentiated (achondrite, group IIIAB iron) parent bodies. IAB and IIICD may be complementary fractional crystallization/partial melting suites from the same parent body. Since the model also explains some unusual irons, it seems for the first time possible to understand the genesis of almost all irons, and link them to the major groups of primitive and differentiated meteorites.